Capped RPI Liabilities, a CPI Switch and an Inflation Swap
A UK defined benefit pension scheme has £1.4bn of technical provisions, of which 70% relates to pensioners already in payment. Pensions in payment increase annually in line with RPI, subject to a cap of 5% and a floor of 0%. The scheme is 92% funded on its technical provisions basis, which assumes RPI of 2.8% a year. Current RPI is 4.6%, ten-year breakeven inflation is 3.4%, and CPI is 3.1%. Assets are 40% nominal gilts, 25% index-linked gilts, 20% equities and 15% corporate bonds. The sponsor has proposed switching future indexation for the small active membership (8% of liabilities) from RPI to CPI, and the trustee is also considering buying a 15-year RPI swap on £300m notional. The scheme actuary has been asked to advise on the modelling needed before either decision is taken.
1. Explain how the 5% cap and 0% floor alter the scheme's economic exposure to inflation, and why a deterministic model using the single 2.8% assumption is not fit for this decision.
Read the worked answer
The promise is not a pure RPI link. The scheme pays an RPI-linked amount capped at 5% a year, which is economically an uncapped RPI liability minus the value of a 5% RPI cap. The 0% floor matters only in deflation: a low-probability but not irrelevant scenario.
With a single deterministic 2.8% assumption the cap never bites, so the model values a fully RPI-linked liability. That overstates the liability in high-inflation scenarios and, more importantly, hides the non-linearity. Because the cap truncates the upside, the liability's sensitivity to inflation depends on the level and volatility of inflation, not just its mean. Duration or convexity measures calibrated on one deterministic path will misstate the exposure.
The appropriate model is a stochastic inflation process (mean-reverting lognormal, or a model calibrated to RPI swaps and inflation caps/floors), with the cap and floor valued as options. Calibrate to the 3.4% ten-year breakeven and to cap/floor prices rather than to a single mean. Include the indexation lag: pensions typically increase by reference to the previous September's RPI, which delays the cash-flow impact. Model the correlation between inflation and nominal yields, and between inflation and asset returns. Report a distribution of the funding level, not one number.
2. Assess whether switching future indexation from RPI to CPI for the 8% active membership is likely to be a material risk reduction, and identify the modelling and non-modelling issues.
Read the worked answer
The direct effect is small. Only 8% of liabilities relate to active members, and only future accrual would switch, so the reduction in total liability is likely to be a few per cent at most. A CPI link is typically around 0.8–1.0% a year below RPI, though the gap has narrowed and is itself uncertain; a fixed differential should not be hard-coded.
The asset side is more important. The scheme holds 25% index-linked gilts, which pay RPI. If liabilities become CPI-linked while assets remain RPI-linked, the scheme is over-hedged against RPI. In a high-RPI scenario assets rise more than liabilities, which sounds benign but creates basis risk and makes the hedge inefficient. The economic risk reduction is therefore smaller than the liability reduction suggests.
Non-modelling issues: the change may require a deed amendment, member consultation and legal advice; the trustee must act in members' interests and consider whether the amendment is permitted. The modelling should use a stochastic RPI–CPI spread and be run alongside alternatives such as buying CPI-linked assets or CPI swaps. Recommendation: treat this as a small, legally constrained measure, not as the main fix for inflation risk.
3. Recommend how the actuary should model the proposed £300m RPI swap purchase, including what should be compared and what risks remain.
Read the worked answer
The swap pays RPI on £300m for 15 years. The first comparison is the swap breakeven (3.4%) against the scheme's own expected RPI. If the scheme expects RPI above 3.4%, the swap appears attractively priced, but most of that difference is an inflation risk premium plus liquidity and collateral premia, not a free expected profit. For funding and regulatory purposes the swap must be valued market-consistently.
Second, the swap is uncapped while the liability is capped at 5%. In high-inflation scenarios the scheme pays RPI on £300m without a matching increase in liability, so it over-hedges precisely when inflation is high. A partial swap, or a swap combined with a purchased cap, would mirror the capped liability better.
Third, £300m covers only about 21% of liabilities: the hedge is partial, and its 15-year term may be shorter than the liability duration. Collateral and counterparty credit risk must be modelled, including margin calls in a rising-rate scenario.
The actuary should compare distributions of the funding level with and without the swap across stochastic inflation and interest rate scenarios, and report the residual basis, cap, term and counterparty risks to the trustee.